課程概述 Course Description
每週對於所指導之研究生所課程安排之討論課程，研究學習微分方程。
We will arrange one discussion per week for each of students.
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先修課程或先備能力 Prerequisite Course(s):
高等微積分，線性代數，微分方程，偏微分方程，計算器，數學軟體Maple, Matlab, Mathematica 等任何一種
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教師聯絡資訊 Contact with Teacher
開課教師：方永富
研究室：數館210室
e-mail：yffang@mail.ncku.edu.tw
電話：275-7575轉65131
授課時間：星期三 9~A
Office Hours：星期一，三：12：10-13：00
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助教資訊 Contact with Tutor
本課程將沒有助教協助研討課，負責講解作業及小考測驗
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課程學習目標 Course Objectives
HUANG-GUO-HENG-2020-Scattering for 3D QZ in L2
Merle-Tsutsumi-1990-L2 concentration of blow-up for NLS with critical power
Ogawa-Tsutsumi-1991-Blow-up-of-H1-solution-for-NLS
Tsutsumi-1990-Rate of L2 concentration of blow-up solutions for the NLS
Local Well Posedness of NLS
Global Existence and Finite-Time Blowup
Stability of Solitary Waves for the quantum Zakharov Equations
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課程進度 Course Outline
In the 1st semester:
週次 Week進度說明 Progress Description
1 Ogawa-Tsutsumi-1991-Blow-up-of-H1-solution-for-NLS
2 Ogawa-Tsutsumi-1991-Blow-up-of-H1-solution-for-NLS
3 HUANG-GUO-HENG-2020-Scattering for 3D QZ in L2
4 HUANG-GUO-HENG-2020-Scattering for 3D QZ in L2
5 HUANG-GUO-HENG-2020-Scattering for 3D QZ in L2
6 Merle-Tsutsumi-1990-L2 concentration of blow-up for NLS with critical power
7 Merle-Tsutsumi-1990-L2 concentration of blow-up for NLS with critical power
8 Tsutsumi-1990-Rate of L2 concentration of blow-up solutions for the NLS
9 Tsutsumi-1990-Rate of L2 concentration of blow-up solutions for the NLS
10 Tsutsumi-1990-Rate of L2 concentration of blow-up solutions for the NLS
11 Guo-Nakanishi-Wang-2013-Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
12 Guo-Nakanishi-Wang-2013-Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
13 Guo-Nakanishi-Wang-2013-Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
14 Guo-Nakanishi-Wang-2013-Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
15 Guo-Nakanishi-Wang-2013-Global dynamics below the ground state energy for the Zakharov system in the 3D radial case
16 Candy-Herr-Nakanishi-2021-GWP for the energy-critical Zakharov system below the ground state
17 Candy-Herr-Nakanishi-2021-GWP for the energy-critical Zakharov system below the ground state
18 Candy-Herr-Nakanishi-2021-GWP for the energy-critical Zakharov system below the ground state
以上每週進度教師可依上課情況做適度調整。 The schedule may be subject to change.
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教學方法 Teaching Strategies
方法 百分比%
講授 Lecture 30
討論 Discussion 70
※請遵守智慧財產權觀念 不得不法影印
Please follow the Intellectual Property instruction and No illegal copy
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課程教材 Course Material
Lecture Notes, Homework, Quizzes ，計算器，數學軟體 Maple, Matlab, Mathematica 等任何一種
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參考書目 References
Partial Differential Equations, An Introduction by Walter Strauss
Partical Differential Equation by Fritz John
Partial Differential Equations by Lawrence Evans
Semilinear Schrödinger equations by Thierry Cazenave
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評量方式 Grading
方法 百分比%
出席 Participation: 5%
口頭報告 Presentation : 70%
作業 Homework: 25%
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學習規範 Course Policy
請遵守智慧財產權觀念不得不法影印
Please follow the Intellectual Property instruction and No illegal copy
1. 作業不能遲交。
2. 缺考需要醫師證明、或家長證明、或學校公假單。
3, 考試違規，報請學校處理。
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課程網址 Course Website:
Moodle and http://www.math.ncku.edu.tw/~fang- 教師(teacher): 方永富